Yue et al. 1

Diversity indices and spatial scales greatly effect the conclusions of

relationships between biodiversity and ecosystem functions

Tian XiangYue,a* Ji Yuan Liu,a Si Qing Chen,a Zheng Qing Li,b Yong Zhong Tiana, Feng Gec

aInstitute of Geographical Sciences and Natural Resources Research, Chinese Academy of Sciences,

100101 Beijing, China (email: Yue@lreis.ac.cn)

bInstitute of Botany, Chinese Academy of Sciences, 100093 Beijing, China

cInstitute of Zoology, Chinese Academy of Sciences, 100080 Beijing, China

Abstract

The relationships between biodiversity and ecosystem functions such as stability and

productivity has long been debated and has no final conclusion until now. But it is ignored that the

debate should be firstly based on the same diversity index, which should be theoretically complete,

and on same observation scale. For the issue on the scale of ecotope observation, ecosystems should

be distinguished according to intensity of human disturbance. For the issue on the scale of species

observation, either number diversity or biomass diversity should be identified. This paper takes

grassland ecosystems located within the Bayin Xile grassland of Xilin Gol League of Inner

Mongolia Autonomous Region as an example and analyzes effects of different diversity indices and

of various spatial scales on the relationships between biodiversity and ecosystem functions. The

calculation results show that different diversity indices lead to different conclusions. The analysis to

land cover data based on Landsat TM images by up-scaling process demonstrates that spatial scale

of data has a great effect on the conclusion of the relationships between biodiversity and ecosystem

functions.

Keywords: Biodiversity; Ecosystem function; Relationship; Diversity index; Spatial scales

Corresponding author: Tel.: +86-10-64889633; Fax: +86-10-64889630. E-mail: yue@LREIS.ac.cn (T. X. Yue)

Yue et al. 2

1. Introduction

Prior to 1970s, ecologists attempted to develop a general theory linking stability and diversity on

the scale of species observation (Odum, 1953; MacArthur, 1955; Elton, 1958; Hutchinson, 1959).

Since Gardner and Ashby (1970) and May (1972) challenged the conventional wisdom that stability

increases with species diversity, the thinking of some scientists started to change gradually. There

appeared two camps on the diversity-stability hypothesis. Some scientists argued that their research

results did not support the conventional wisdom of natural historians: diversity begets stability

(Gilpin, 1975; Woodward, 1994; Beeby and Brennan, 1997; Naeem, 2002; Pfisterer and Schmid,

2002; Lhomme and Winkel, 2002). However, many scientists still believe that diversity begets

stability (Odum, 1971; Watt, 1973; McNaughton, 1978; Glowka et al., 1994; Pennist, 1994;

McGrady et al., 1997; Naeem and Li, 1997; Tilman et al., 1997). In particular, many recent

advances have indicated that diversity can be expected, on average, to give rise to ecosystem

stability (Wolfe, 2000; Chapin III et al., 2000; Tilman, 2000; Bengtsson et al., 2000; McCann,

2000).

The relationship between diversity and productivity has been a central but contentious issue

within ecology (Schmid, 2002). In terms of Darwin’s result, the biodiversity of communities is due

to niche diversification of the co-occuring species and such diversification will lead to greater

community productivity due to more effective resource exploitation (Darwin, 1872). In 1968, the

evidence from California grasslands showed that net productivity was inversely related to species

diversity (McNaughton, 1978), which challenged Darwin’s result. Since 1990s, there have appeared

ardent debates on the diversity-productivity relationships. New York successional analyses

suggested that average net productivity was negatively related to species diversity (McNaughton,

1993). Johnson et al. (1996) argued that attempts to unveil the relationships between biodiversity

and ecosystem productivity continue to generate contradictory conclusions. Rusch and Oesterheld

(1997) claimed that diversity has a negative effect on productivity. Wardle et al. (1997) concluded

that species composition, rather than species diversity, is the main determinant of ecosystem

productivity. Hooper and Vitousek (1997) in terms of their experiment in a grassland in California

debated that primary productivity did not correlate with increasing functional group richness, but

Yue et al. 3

composition explained much more variance than did richness. Grime (1997) stated that dominant

plants rather than biodiversity control ecosystem productivity. Huston et al. (2000) concluded that

species richness per se has no statistically or biologically significant effect on plant productivity.

However, many ecologists still believe Darwin’s result. The experimental results at eight European

field sites showed that each halving of the number of plant species reduced productivity by

approximately 80gm-2 on average (Hector et al., 1999). Tilman (2000) reviewed recent experimental,

theoretical and observational studies and stated that on average greater diversity leads to greater

productivity in plant communities, greater nutrient retention in ecosystems and greater ecosystem

stability. Purvis and Hector (2000) summarized that 95% of experimental studies support a positive

relationship between diversity and ecosystem functioning. Many ecologists (Tilman et al., 2001;

Swift and Anderson, 1993; Lehman and Tilman, 2000; Loreau, 2000; Loreau and Hector, 2001)

think that productivity may be greater at higher diversity because of niche complementarity among

particular combinations of species and the greater chance of occurrence of such combinations at

higher diverity. Cardinale et al.’s experiment (2002) showed that bryophyte diversity and

productivity have a positive relationship because a greater complexity of vertical structure helps to

trap water and facilitate plant survival during drought. Pfisterer and Schimid (2002) in their

combinatorial biodiversity experiments found that higher diversity tends to lead to higher

productivity.

On the scale of ecotope observation (Naveh and Lieberman, 1994; Forman, 1995), Odum (1969)

proposed the strategy of ecosystem development and stated that the most pleasant and certainly the

safest landscape to live in is one containing a variety of crops, forests, lakes, streams, roadsides,

marches, seashores, and ‘waste places’. Haber (1971) applied this strategy into land utilization

systems and proposed the concept of differentiated land use (Haber, 1979) and a differentiated land

use strategy (Haber, 1990). Numerous authors have stressed the favorable effect of diversity on

agroecosystem functions such as ecosystem stability and productivity (Mager, 1985; Kaule, 1986;

Barbier, 1990; Francis and Clegg, 1990; Stinner and Blair, 1990; Stocking et al., 1990; Altieri, 1991;

Prinsley, 1992; Ryszkowski, 1992; Yue and Jiang, 1993; Nachtigall, 1994; Yue and Kong, 1994;

Ripl, 1995; Burel, 1996; Lenz and Haber, 1996; Herzog, 1997; Pfiffner, 1996; OECD, 1997).

Yue et al. 4

However, most of the arguments on the relationships between biodiversity and ecosystem

functions do not clear what kind of diversity index is used and how large spatial scale or how high

spatial resolution of data their calculations are based on.

2. Methods

2.1 Study region

The investigated region with total area of 97200 hectares is located in

91'4643 44'2943 Noo ′′−′′ and 33'491163'25116 Eoo ′′−′′ , within the Bayin Xile Grassland of

Xilin Gol League of Inner Mongolia Autonomous Region. It has a semi-arid and continental

grassland climate in temperate zone. The annual average temperature is 0.2oC, with a highest

temperature of 38.5oC in summer and a lowest temperature of –42.8oC in winter. The annual

average precipitation is 350mm. The most common species are Aneurolepidium chinensis (Trin.)

Kitag. and Stipa grandis P. Smirn., of which biomass accounts for 60.4% of the total amount.

Precisely, Aneurolepidium chinensis (Trin.) Kitag. accounts for 48.8% and Stipa grandis P.

Smirn.11.6%. Grass plants return green at the end of April and senescence in early October. Plant

growing period lasts about 150 days.

2.2 Data acquisition of land cover

Landsat TM/ETM images, taken on 31 July of 1987, 11 August of 1991, 27 September of 1997,

and 23 May of 2000, are analyzed by applying digital image processing techniques to the 6

visible/near-infrared bands (bands 1, 2, 3, 4, 5, and 7). Ancillary data include a vegetation map of

Bayin Xile, a soil map of Xilin River Basin, a topographical map, and biomass data sampled in the

field. Using the 6 atmospherically-corrected bands as input, 48 spectral classes are generated by

unsupervised classification procedure of ISODATA (ERDAS/Imagine 8.4 package). Because

cropland and wetland could not be separated out as unique spectral classes, supervised classification

is used to define training samples of cropland and wetland. The supervised training samples and the

48 unsupervised spectral classes are combined together and the whole image is classified again by

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using the maximum likelihood classification procedure. Using the ancillary data as a reference, the

spatial relationships between spectral classes and land cover types are established. The final land

cover classification map has 14 identical classes: F. sibiricum steppe, S. baicalensis steppe, A.

chinensis + forbs steppe, A. chinensis + bunchgrasss steppe, A. chinensis + Ar. frigidas steppe, S.

grandis + A. chinensis steppe, S. grandis + bunchgrasss steppe, S. krylavii steppe, Ar. frigida steppe,

cropland, wetland, desertification land, saline-alkaline land, and water area (as seen in Figures 1, 2,

3, and 4).

Fig. 1. Land Cover in 1987 (30m×30m)

Fig. 2. Land Cover in 1991 (30m×30m)

Fig. 3. Land Cover in 1997 (30m×30m)

Fig. 4. Land Cover in 2000 (30m×30m)

2.3 Data acquisition of maximum aboveground biomass in terms of species

The peak value of aboveground biomass of the grass communities appears at the end of August

usually, which is considered as the grassland productivity. In order to analyze the relationship

between species biomass diversity and the grassland productivity, 57 sampling quadrates that all

sizes are mm 11 × were randomly selected. The sampling process includes 5 steps: (1) cutting

grass to the roots at the end of August, (2) classifying the cut grass in terms of species, (3) drying

the cut grass in terms of species at 60oC, and (4) weighting the dried grass in terms of species. Inner

Mongolia Grassland Ecosystem Research Station, which was founded in 1979 and was

listed as a key project demonstrative station by UNESCO’s MAB program in 1988, has been

repeating the sampling process in the study region at the end of August every year since 1980. We

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only pay an attention to the data selected in 1987, 1991, 1997 and 2000 in order to correspond with

the land cover data.

2.4 Diversity indices

Twenty-seven diversity indices can be found in literatures (Yue et al., 1998; 2001; 2003). In

addition to a scaling index introduced recently,

( )( )( )

( )

( )ε

ε

ln

ln2

1

21

−=∑

=

m

ii tp

td

the most widely used diversity indices in ecological literature include Shannon’s index,

( ) ( )( )

( )tptptI i

m

ii ln

1∑

=

−=ε

,

and Simpson’s index,

( ) ( )( )( ) 1

1

2−

=

= ∑

εm

ii tptS

where ( )tpi is probability of the ith investigation object such as species biomass or ecotope;

( )εm is total number of the investigation objects; t represents time variable; sae +=

ε1

, a is area

of studied region in hectares, s is spatial resolution of land cover data or area of sampling quadrat,

and e equals 2.71828.

3. Results

3.1 Different diversity index leads to different conclusions on relationships between

biodiversity and ecosystem functions

The calculation results by operating the three diversity indices on the sampling data in the field

in 1987, 1991, 1997 and 2000 (as seen in Table 1) shows that correlation coefficients of scaling

diversity, Shannon’s diversity, and Simpson’s diversity (Table 2) with grassland productivity are

Yue et al. 7

respectively 0.83, 0.69, and 0.38 (Table 3). In other words, if scaling index is used it could be

concluded that species biomass diversity has positive relation with grassland productivity; but if

Simpson’s index is used it is difficult to be concluded that species biomass diversity has a positive

relation with grassland productivity.

Table 1. The sampling data of maximum aboveground biomass (g/m2)

Table 2. Grassland productivity and species biomass diversity

Table 3. Correlation of productivity with species biomass diversity and ecotope diversity

The calculation results by operating the diversity indices on the land cover data at 30m×30m

resolution (Fig. 1-4) show that scaling diversity and Shannon’s diversity have no relationship with

grassland diversity, but correlation coefficient between Simpson’s diversity and grassland

productivity is 0.68. Statistically, the calculation results by the three diversity indices have different

trends from 1987 to 2000. Shannon’s diversity and scaling diversity have an increase trend from

1991 to 1997, but Simpson’s diversity has a decrease trend in this period. From 1997 to 2000,

Shannon’s diversity and Simpson’s ecotope diversity have an increase trend, but scaling diversity

has no change (Table 4). Correlation coefficient between ecotope diversity and desertification area

for scaling index, Shannon’s index, and simpson’s index are respectively 0.96, 0.93, and 0.71, so

that we can conclude that ecotope diversity increase leads to ecosystem unstability.

Table 4. Desertification area and ecotope diversity

3.2 Spatial scale of data has a great effect on the conclusion of the relationships

between biodiversity and ecosystem functions

The land cover data set on 30m×30m spatial resolution is transformed into 20 more ones by

Yue et al. 8

up-scaling process (Table 5, 6, and 7). The pixel side of every new land cover data set is 30m bigger

than the transformed one both in width and height. The land cover type in each pixel of the new land

cover data is derived from the dominant land cover type of the transformed pixels. When every new

data set is created, it can be export to a vector polygon file such as Coverage of Arc/Info.

Table 5. Effect of different spatial scales on correlation coefficient of scaling diversity with grassland

productivity and desertification area

Table 6. Effect of different spatial scales on correlation coefficient of Shannon’s diversity with grassland

productivity and desertification area

Table 7. Effect of different spatial scales on correlation coefficient between Simpson’s diversity and grassland

productivity

The analysis results show that pixel size change causes nonlinear change of correlation

coefficients of ecotope diversity with grassland productivity and desertification area, in which

enlargement of desertification area indicates unstability of the grassland ecosystem. When pixel size

is 210m×210m correlation coefficients between ecotope diversity and grassland productivity reach

maximum values for all of scaling index, Shannon’s index and Simpson’s index, which are 0.52,

0.75 and 0.89 respectively. But correlation coefficients between ecotope diversity and desertification

area reach maximum values for all of the three indices when pixel size is 30m×30m; correlation

coefficient between ecotope diversity and desertification area reaches maximum value for

Simpson’s index when pixel size is 60m×60m. Therefore, at spatial resolution 210m×210m we

conclude that higher ecotope diversity tends to lead to higher productivity; at 30m×30m there is an

inverse relationship between ecotope diversity and ecosystem stability.

4. Discussions

Yue et al. 9

Unsatisfying diversity indices have been criticized by many specialists. For instance, Odum

(1969) stated that Shannon’s formula may obscure the behavior of these two rather different aspects

of diversity, variety and evenness. Pimm (1994) reviewed the research history of relation between

diversity and stability and concluded that theoretical studies of whether interacting sets of species

will be stable consider whether the densities of all those species return to equilibrium or not. To ask

how long a community persists before it is invaded is to ask how long the community composition

lasts. Such a discussion ignores fluctuations in the abundance of species, i.e. equitability, and looks

only at the species list itself. Harper and Hawksworth (1996) pointed out that Shannon diversity

index and Simpson’s index are inadequate for some purposes because it is possible for a species-rich

or ecotope-rich but inequitable community to have a lower index than one that is less species-rich or

less ecotope-rich but highly equitable. Hooper and Vitousek (1997) stated that species diversity

measured by Shannon index ignores species composition. Beeby and Brennan (1997) described that

various indices attempt to measure diversity and include some measure of equitability, with varying

success. In doing so, the index may make assumptions about the underlying pattern of equitability

within the community, which itself can be problematical. Yue et al (1999) found that Shannon index

could not express the ‘variety’ component of diversity and does not imply any information of the

size of the area under investigation region; if Shannon index is used the number of every species or

every ecotope type should be greater than 100 theoretically. Therefore, the scaling index was

introduced on the basis of theoretical demonstration, for which all diversity indices were analyzed

(Yue et al., 1998). Although the scaling index has been tested and improved many times (Yue et al.,

1999, 2000, 2001, 2002, 2003), its effectiveness under all circumstances does still need to be further

tested.

Effects of spatial scale on biodiversity and on relationships between biodiversity and ecosystem

functions have been discussed by many specialists. For instance, Noordwijk’s results (2002) showed

that intensification of crop-fallow system is likely to decrease the average species richness per unit

area at field scale, but ecotope diversity may initially increase; while further intensification is likely

reduce all aspects of biodiversity. Gotelli (2002) stated that species diversity is a challenging

parameter to measure because diversity is organized hierarchically: individual organisms are

Yue et al. 10

classified into species, species into genera, and genera into families, and so on. Enquist and Niklas

(2001) found that organizing principles are needed to link biodiversity across spatial and temporal

scales. Crawley and Harral (2001) demonstrated that different processes might determine plant

biodiversity at different spatial scales. Ritchie and Olff (1999) proposed that the spatial scaling of

resource use by species of different size may explain many species-diversity patterns across a range

of spatial scales, which seems to provide a basis for the development of ecological theories that are

trans-scalar in geographical space (Whittaker, 1999). Our results show that species diversity is much

smaller than ecotope diversity in the investigated region within the Bayin Xile Grassland. This

means that the sampling process might not cover all species in the region. These problems caused by

incomplete and uneven sampling expect to be solved by means of remote sensing (Nagendra and

Gadgil, 1999; Yue, 2000; Yue and Liu, 2003).

Many specialists noted that relationships between biodiversity and ecosystem functions require

particular attention on various scales such as local, landscape and regional ones. For instances,

Chase and Leibold (2002) concluded that the shape of the productivity-biodiversity relationship

depends on spatial scale; when data were viewed among ponds the relationship between species

diversity and productivity was hump-shaped, whereas the same data were viewed among watersheds

the relationship was positively linear. Noordwijk’s result (2002) showed that trade-off between

productivity and biodiversity depend on the scale of model application. Loreau, et al. (2001) stated

that generally the relative effects of individual species and species richness may expected to be

greatest at small-to-intermediate spatial scales, but these biological factors should be less important

as predictors of ecosystem processes at regional scales, where environmental heterogeneity is

greater. Purvis and Hector (2000) found that the relationship between plant diversity and

productivity changes with spatial scales. Gaston (2000) stated that observed patterns may vary with

spatial scales and processes at regional scales influence patterns observed at local ones. Results of

plant diversity and productivity experiments in European grasslandshighlighted the importance of

considering scale when studying relationship between diversity and productivity (Hector et al.,

1999). Our results showed that spatial resolution of data have a nonlinear effect on the relationships

between diversity and ecosystem functions such as productivity and stability (Fig.5 and Fig.6).

Yue et al. 11

Fig.5 Effects of spatial resolution on correlation coefficient between diversity and productivity

Fig.6 Effects of spatial resolution on correlation coefficient between diversity and desertification area

In short, discussions on the relationships between diversity and ecosystem functions should be

based on specific diversity index and on specific spatial scale or spatial resolution of data.

ACKNOWLEDGEMENTS

This work is supported by National Basic Research Priorities Program (2002CB412500-6) of

Ministry of Science and Technology of the People's Republic of China and Project (90202002) of

National Natural Science Foundation of China.

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Table 1. The sampling data of maximum aboveground biomass (g/m2) Species 1987 1991 1997 2000 Aneurolepidium chinensis (Trin.) Kitag. 60.63 117.27 88.21 129.343 Stipa grandis P. Smirn. 26.57 22.2 7.25 23.8605 Achnathrum sibiricum (L.) Keng 6.55 6.44 1.09 14.503 Caragana microphylla Lam. 13.96 4.39 0 3.398 Agropyron michnoi Roshev 6.12 20.53 0 2.708 Artemisia commutata Bess. 31.87 9.6 0.51 0.846 Carex korshinshyi Kom. 4.44 0.43 6.51 37.725 Artemisia scoparia Wald. et Kit. 0 0 0 0.284 Salsola collina Pall. 0.07 0.16 0 0 Kochia prostrata (L.) Schrad. 3.01 1.5 0.23 8.1155 Serratula centeuroides L. 1.92 0.72 0.72 2.8265 Artemisia frigida Willd. 1.35 1.72 0.67 1.128 Cleistogenes squarrosa (Trin.) Keng 0.54 1.12 2.39 2.863 Koeleria cristata (L.)Pers. 1.28 3.69 0.92 9.4275 Heteropappus altaicus (Willd.) Novopokr. 2.69 1.64 0.48 0.059 Poa palustris L. 0.29 3.73 1.31 1.3835 Allium ramosum L. 0 0.15 4.92 0.225 Allium senescens L. 5.47 6.83 0 6.914 Potentilla tanacetifolia Willd. Ex Schlecht. 0.8 0.15 1.15 2.6355 Melissitus ruthenica (L.) Peschkova 0.5 0.04 1.27 1.1065 Orostachys fimbriatus (Turcz.) Berger 0.36 0.74 0.17 0 Allium tenuissimum L. 0.76 2.78 0 3.0445 Potentilla acaulis L. 0 0 1.41 3.1735 Allium bidentatum Fisch. ex Prokh. 0.18 0.09 0 0.6055 Dontostemon micranthus C. A. Mey 1.25 1.43 0 0 Allium condensatum Turcz. 0 0.58 0.31 0.513 Saposhnikovia divaricala (Turca.) Schischk. 0.35 0 0.21 1.108 Artemisia sieversiana Willd. 6.17 0 0 0 Potentilla bifurica L. 1.27 0 0.53 1.334 Allium anisopodium Ldb. 0.11 1.48 0 3.8515 Oxytropis myriophylla (Pall.) DC. 0.72 0.03 0 0 Elymus dahuricus var. tangutorum Roshev. 0 0 0.25 0 Astragalus adsurgens Pall. 0 0 0 0.001 Thalictrum petaloideum var. 0.77 0.36 0.04 0.002 Chenopodium glaucum L. 0 0.14 0 0 Pulsatilla tenuiloba (Turcz.) Tuz. 0 0.19 0 1.148 Thermopsis lanceolata R. Br. 0 0 0 0.2285 Adenophora stenanthina (Ldb.) Kitag. 0 0 0 2.985 Haplophyllum dauricum Juss. 0.05 0 0 0.0255 Iris tenuifolia Pall. 0 0 0 0.0535 Melandrium brachypetalium (Horn) Fenzl. 0.01 0 0 0 Potentilla verticillaris Steph. ex Willd. 0 0 0 0.695 Cymbaria dahurica L. 0.13 0 0 0 Adenophora crispata (Korsh.) Kitag. 0 0 0.01 0.4995 Gueldenstaedtia verna (Georgi) A. Bor. 0 0 0.06 0 Astragalus galactites Pall. 0 0 0 0.001 Chenonpodium aristatum L. 0 0.12 0 0 Gentiana squarrosa Ldb. 0 0.02 0 0 Others 0.05 0 0 4.98

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Table 2. Grassland productivity and species biomass diversity

Year Biomass (g/m2) Species biomass diversity

Scaling index Shannon’s index Simpson’s index1987 180.24 0.13 2.21 2.491991 210.27 0.12 1.76 1.711997 120.62 0.10 1.23 1.352000 274.20 0.14 2.08 1.98

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Table 3. Correlation of productivity with species biomass diversity and ecotope diversity Diversity index name Species biomass diversity Ecotope diversity (30m×30m resolution) Scaling index 0.83 -0.08 Shannon’s index 0.69 0.17 Simpson’s index 0.38 0.69

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Table 4. Desertification area and ecotope diversity

Year Desertification area (hectare)

Ecotope diversity (30m×30m resolution)

Scaling index Shannon’s index Simpson’s index 1987 357.12 0.53 8.76 86.35 1991 930.78 0.54 9.37 422.20 1997 2503.98 0.55 9.71 298.18 2000 2986.56 0.55 9.77 585.14

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Table 5. Effect of different spatial scales on correlation coefficient of scaling diversity with grassland productivity and desertification area Ordinal number Pixel size Year Correlation coefficient

1987 1991 1997 2000 With productivity With desertification area

1 30m×30m 0.53 0.54 0.55 0.55 -0.08 0.96 2 60m×60m 0.49 0.49 0.50 0.50 0.08 0.90 3 90m×90m 0.44 0.46 0.46 0.46 0.32 0.82 5 120 m×120m 0.41 0.43 0.43 0.43 0.39 0.79 6 150m×150m 0.39 0.41 0.40 0.41 0.46 0.76 7 180m×180m 0.37 0.39 0.38 0.39 0.43 0.75 8 210m×210m 0.35 0.37 0.37 0.38 0.52 0.73 9 240m×240m 0.34 0.36 0.35 0.36 0.42 0.72 10 270m×270m 0.32 0.35 0.34 0.35 0.43 0.69 11 300m×300m 0.31 0.34 0.33 0.34 0.41 0.70 12 330m×330m 0.30 0.33 0.32 0.33 0.35 0.69 13 360m×360m 0.29 0.32 0.31 0.32 0.38 0.75 14 390m×390m 0.28 0.31 0.30 0.31 0.36 0.66 15 420m×420m 0.27 0.30 0.29 0.30 0.46 0.64 16 450m×450m 0.27 0.29 0.29 0.30 0.37 0.69 17 480m×480m 0.26 0.28 0.29 0.29 0.25 0.79 18 510m×510m 0.25 0.29 0.28 0.28 0.38 0.62 19 540m×540m 0.25 0.28 0.27 0.28 0.48 0.62 20 570m×570m 0.24 0.27 0.26 0.27 0.40 0.64 21 600m×600m 0.24 0.27 0.26 0.27 0.38 0.48

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Table 6. Effect of different spatial scales on correlation coefficient of Shannon’s diversity with grassland productivity and desertification area

Ordinal number Pixel size Year Correlation coefficient

1987 1991 1997 2000 With productivity With desertification area

1 30m×30m 8.76 9.37 9.71 9.77 0.17 0.93 2 60m×60m 8.13 8.78 8.88 9.02 0.28 0.85 3 90m×90m 7.30 8.09 7.91 8.31 0.52 0.73 5 120 m×120m 6.73 7.57 7.30 7.78 0.58 0.69 6 150m×150m 6.32 7.17 6.75 7.33 0.67 0.59 7 180m×180m 5.91 6.85 6.39 6.97 0.64 0.57 8 210m×210m 5.64 6.55 5.96 6.73 0.75 0.51 9 240m×240m 5.42 6.29 5.85 6.44 0.67 0.58 10 270m×270m 5.21 6.12 5.50 6.22 0.74 0.46 11 300m×300m 4.96 5.94 5.35 6.05 0.70 0.50 12 330m×330m 4.77 5.78 5.24 5.82 0.63 0.52 13 360m×360m 4.67 5.57 5.02 5.63 0.69 0.48 14 390m×390m 4.50 5.52 4.87 5.37 0.60 0.37 15 420m×420m 4.44 5.38 4.73 5.37 0.70 0.41 16 450m×450m 4.23 5.26 4.64 5.23 0.65 0.44 17 480m×480m 4.07 5.07 4.69 5.15 0.55 0.61 18 510m×510m 4.08 5.16 4.47 5.05 0.63 0.39 19 540m×540m 4.08 5.04 4.32 4.91 0.68 0.31 20 570m×570m 3.89 4.89 4.11 4.79 0.71 0.31 21 600m×600m 3.86 4.95 4.10 4.67 0.63 0.22

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Table 7. Effect of different spatial scales on correlation coefficient between Simpson’s diversity and grassland productivity

Ordinal number Pixel size Year Correlation coefficient

1987 1991 1997 2000 With productivity With desertification area

1 30m×30m 86.35 422.20 298.18 585.14 0.68 0.71 2 60m×60m 85.32 284.89 312.16 444.36 0.48 0.89 3 90m×90m 69.25 227.20 124.91 322.94 0.82 0.60 5 120 m×120m 60.78 182.26 72.16 248.79 0.89 0.47 6 150m×150m 53.57 162.16 51.76 167.87 0.85 0.26 7 180m×180m 46.16 147.56 43.75 125.68 0.76 0.12 8 210m×210m 43.18 126.99 24.72 134.59 0.89 0.18 9 240m×240m 40.81 108.86 37.66 126.70 0.89 0.33 10 270m×270m 38.01 102.35 20.30 101.85 0.88 0.12 11 300m×300m 33.57 93.39 19.37 93.57 0.88 0.14 12 330m×330m 29.89 84.60 19.74 80.04 0.85 0.12 13 360m×360m 31.13 77.65 16.52 60.21 0.76 -0.09 14 390m×390m 24.55 82.62 15.86 47.67 0.57 -0.19 15 420m×420m 27.31 70.79 16.47 55.59 0.76 -0.06 16 450m×450m 21.48 67.28 13.75 45.40 0.66 -0.11 17 480m×480m 19.51 58.13 17.52 49.07 0.76 0.09 18 510m×510m 18.93 67.99 13.65 47.78 0.68 -0.05 19 540m×540m 19.43 63.17 12.71 38.19 0.60 -0.17 20 570m×570m 18.20 55.95 9.88 35.45 0.64 -0.17 21 600m×600m 17.20 59.43 10.60 32.23 0.54 -0.22

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Fig. 1. Land Cover in 1987(30m×30m)

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Fig. 2. Land Cover in 1991 (30m×30m)

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Fig.3 Land Cover in 1997(30m×30m)

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Fig.4 Land Cover in 2000 (30m×30m)

- 0. 2

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Fig.5 Effects of spatial resolution on correlation coefficient between diversity and productivity

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Fig.6 Effects of spatial resolution on correlation coefficient between diversity and desertification area